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Sep 23, 2013
09/13

by
András Némethi

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We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of relative sections of line bundles (proving that the equivariant, divisorial multi-variable Hilbert series is topological), a combinatorial description of divisors of analytic function-germs, and an expression for the multiplicity of the singularity from its...

Source: http://arxiv.org/abs/0810.4129v1

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Jun 28, 2018
06/18

by
András Némethi

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We prove that the link of a complex normal surface singularity is an L--space if and only if the singularity is rational. This via a recent result of Hanselman, J. Rasmussen, S. D. Rasmussen and Watson (proving the conjecture of Boyer, Gordon and Watson), shows that a singularity link is not rational if and only if its fundamental group is left-orderable if and only if it admits a coorientable taut foliation.

Topics: Algebraic Geometry, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1510.07128

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Sep 21, 2013
09/13

by
Andras Nemethi

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For any negative definite plumbed 3-manifold M we construct from its plumbed graph a graded Z[U]-module. This, for rational homology spheres, conjecturally equals the Heegaard-Floer homology of Ozsvath and Szabo, but it has even more structure. If M is a complex singularity link then the normalized Euler-characteristic can be compared with the analytic invariants. The Seiberg--Witten Invariant Conjecture is discussed in the light of this new object.

Source: http://arxiv.org/abs/0709.0841v1

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Sep 22, 2013
09/13

by
Andras Nemethi

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The main goal of the present article is the computation of the Heegaard Floer homology introduced by Ozsvath and Szabo for a family of plumbed rational homology 3-spheres. The main motivation is the study of the Seiberg-Witten type invariants of links of normal surface singularities.

Source: http://arxiv.org/abs/math/0310083v2

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Sep 17, 2013
09/13

by
András Némethi

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We consider a connected negative definite plumbing graph, and we assume that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg-Witten invariant of this manifold. The first one is the constant term of a `multivariable Hilbert polynomial', it reflects in a conceptual way the structure of the graph, and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface...

Source: http://arxiv.org/abs/1003.1254v2

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Sep 20, 2013
09/13

by
Andras Nemethi

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We compute the Heegaard Floer homology of an oriented 3-manifold obtained by a negative rational surgery along an arbitrary algebraic knot.

Source: http://arxiv.org/abs/math/0410570v1

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Sep 22, 2013
09/13

by
Andras Nemethi

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Recently L. Nicolaescu and the author formulated a conjecture which relates the geometric genus of a complex analytic normal surface singularity (whose link $M$ is a rational homology sphere) with the Seiberg-Witten invariant of $M$ associated with the ``canonical'' $spin^c$ structure of $M$. Since the Seiberg-Witten theory of the link $M$ provides a rational number for any $spin^c$ structure it was a natural challenge to search for a complete set of conjecturally valid identities, which...

Source: http://arxiv.org/abs/math/0310084v1

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Sep 22, 2013
09/13

by
András Némethi

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We establish two exact sequences for the lattice cohomology associated with non-degenerate plumbing graphs. The first is the analogue of the surgery exact triangle proved by Ozsvath and Szabo for the Heegaard-Floer invariant HF^+; for the lattice cohomology over Z_2-coefficients it was proved by J. Greene. Here we prove it over the integers, and we supplement it by some additional properties valid for negative definite graphs. The second exact sequence is an adapted version which does not mix...

Source: http://arxiv.org/abs/1001.0640v2

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Sep 22, 2013
09/13

by
András Némethi

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The article starts with some introductory material about resolution graphs of normal surface singularities (definitions, topological/homological properties, etc). We then discuss the case when the normal surface singularity is an N-fold cyclic covering of a surface germ, branched along a curve given by the germ of an analytic function f. We present non-trivial examples in order to show that from the embedded resolution graph G of f in general it is not possible to recover the resolution graph...

Source: http://arxiv.org/abs/math/0003084v1

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Sep 23, 2013
09/13

by
András Némethi

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We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to find the `limits' of these identities. Connections with the Seiberg-Witten Invariant Conjecture and Semigroup Density Conjecture are discussed.

Source: http://arxiv.org/abs/0710.0987v1

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Sep 17, 2013
09/13

by
Robert Mendris; Andras Nemethi

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We consider suspension hypersurface singularities of type g=f(x,y)+z^n, where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for two pathological cases, which can be completely described. Even in the pathological cases, the link and the Milnor number of g determine uniquely the Newton pairs of f and n. In particular, for such g, we verify Zariski's conjecture about the multiplicity....

Source: http://arxiv.org/abs/math/0207212v1

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Sep 18, 2013
09/13

by
Gabor Braun; Andras Nemethi

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We derive a cut-and-paste surgery formula of Seiberg--Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion formula [arXiv:math.AG/0610464, 4.5] targeting analytic invariants of splice quotient singularities. The two formulas combined provide automatically a proof of the equivariant version [arXiv:math.AG/0310084, 5.2(b)] of the `Seiberg--Witten invariant conjecture' [arXiv:math.AG/0111298] for these singularities.

Source: http://arxiv.org/abs/0704.3145v2

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Jun 27, 2018
06/18

by
József Bodnár; András Némethi

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We prove an additivity property for the normalized Seiberg-Witten invariants with respect to the universal abelian cover of those 3-manifolds, which are obtained via negative rational Dehn surgeries along connected sum of algebraic knots. Although the statement is purely topological, we use the theory of complex singularities in several steps of the proof. This topological covering additivity property can be compared with certain analytic properties of normal surface singularities, especially...

Topics: Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1505.03005

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89

Sep 19, 2013
09/13

by
A. Dimca; A. Némethi

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We show that the monodromy operator at infinity plus the decomposition of the homology given by the vanishing cycles completely determine the homology monodromy representation of any complex polynomial.

Source: http://arxiv.org/abs/math/9912072v2

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Jun 30, 2018
06/18

by
Eugene Gorsky; András Némethi

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We prove that a sufficiently large surgery on any algebraic link is an L-space. For torus links we give a complete classification of integer surgery coefficients providing L-spaces.

Topics: Algebraic Geometry, Mathematics, Geometric Topology

Source: http://arxiv.org/abs/1403.3143

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Sep 23, 2013
09/13

by
Dmitry Kerner; András Némethi

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An old conjecture of Durfee 1978 bounds the ratio of two basic invariants of complex isolated complete intersection surface singularities: the Milnor number and the singularity (or geometric) genus. We give a counterexample for the case of non-hypersurface complete intersections, and we formulate a weaker conjecture valid in arbitrary dimension and codimension. This weaker bound is asymptotically sharp. In this note we support the validity of the new proposed inequality by its verification in...

Source: http://arxiv.org/abs/1109.4869v4

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4.0

Jun 30, 2018
06/18

by
József Bodnár; András Némethi

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We show a counterexample to a conjecture of de Bobadilla, Luengo, Melle-Hern\'{a}ndez and N\'{e}methi on rational cuspidal projective plane curves. The counterexample is a tricuspidal curve of degree 8. On the other hand, we show that if the number of cusps is at most 2, then the original conjecture can be deduced from the recent results of Borodzik and Livingston and (lattice cohomology) computations of N\'emethi and Rom\'an. Then we formulate a `simplified' (slightly weaker) version, more in...

Topics: Mathematics, Algebraic Geometry

Source: http://arxiv.org/abs/1405.0437

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53

Sep 22, 2013
09/13

by
A. Nemethi; M. Tosun

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In the present article we determine and characterize completely the support genus, the binding number and the norm of a page of an open book under the following restrictions: M is a rational homology sphere which can be realized as the link of a surface singularity. Moreover, we restrict ourselves to the collection of those open book decompositions which can be realized as Milnor fibrations determined by some analytic germ (the so-called Milnor open books).

Source: http://arxiv.org/abs/0906.1948v2

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Sep 23, 2013
09/13

by
Dmitry Kerner; Andras Nemethi

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We address the conjecture of [Durfee1978], bounding the singularity genus, p_g, by a multiple of the Milnor number, \mu, for an n-dimensional isolated complete intersection singularity. We show that the original conjecture of Durfee, namely (n+1)!p_g\leq \mu, fails whenever the codimension r is greater than one. Moreover, we propose a new inequality, and we verify it for homogeneous complete intersections. In the homogeneous case the inequality is guided by a `combinatorial inequality', that...

Source: http://arxiv.org/abs/1111.1411v3

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108

Jul 19, 2013
07/13

by
Maciej Borodzik; Andras Nemethi

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Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the (normalized) real Seifert matrix. We study their basic properties, we express the Tristram-Levine signatures and the higher order Alexander polynomial in terms of them. Motivated by singularity theory, we also introduce the spectrum of the link (determined from...

Source: http://arxiv.org/abs/1005.2084v2

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101

Sep 23, 2013
09/13

by
Maciej Borodzik; András Némethi

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We compute the Heegaard Floer homology of $S^3_1(K)$ (the (+1) surgery on the torus knot $T_{p,q}$) in terms of the semigroup generated by $p$ and $q$, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsvath--Szabo d-invariant. We relate the result to known knot invariants of $T_{p,q}$ as the genus and the Levine--Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard Floer homologies of (+1) and (-1) surgeries on torus knots. This...

Source: http://arxiv.org/abs/1105.5508v1

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64

Sep 22, 2013
09/13

by
András Némethi; Ágnes Szilárd

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In this article we give a construction of the resolution graphs of hypersurface surface singularities (X_k,0) given by generalized Iomdin series. All these resolution graphs are coordinated by an ``universal bi-colored graph'' which is associated with the ICIS determining the Iomdin series. The definition of this new graph is rather involved, and in concrete examples it is difficult to compute. Nevertheless, we present a large number of examples. This is very helpful in the exemplification of...

Source: http://arxiv.org/abs/math/0003085v1

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48

Jul 20, 2013
07/13

by
Gabor Braun; Andras Nemethi

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We recover the Newton diagram (modulo a natural ambiguity) from the link for any surface hypersurface singularity with non-degenerate Newton principal part whose link is a rational homology sphere. As a corollary, we show that the link determines the embedded topological type, the Milnor fibration, and the multiplicity of such a germ. This proves (even a stronger version of) Zariski's Conjecture about the multiplicity for such a singularity.

Source: http://arxiv.org/abs/math/0609093v3

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85

Sep 23, 2013
09/13

by
Fouad Elzein; András Némethi

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Let Y be a normal crossing divisor in the smooth projective algebraic variety X (defined over ${\mathbb C}$) and let U be a tubular neighbourhood of Y in X. We construct homological cycles generating $H_*(A,B)$, where (A,B) is one of the following pairs $(Y,\emptyset)$, (X,Y), (X,X-Y), $(X-Y,\emptyset)$ and $(\partial U,\emptyset)$. The construction is compatible with the weights in $H_*(A,B,{\mathbb Q})$ of Deligne's mixed Hodge structure.

Source: http://arxiv.org/abs/math/9909008v1

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38

Sep 23, 2013
09/13

by
András Némethi; Willem Veys

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The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient spaces. That is, we treat in a conceptual unity the poles of the (generalized) topological zeta function and the monodromy eigenvalues associated with a complex analytic function germ f defined on a normal surface singularity (X,0). The article targets the...

Source: http://arxiv.org/abs/1112.1230v1

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54

Sep 18, 2013
09/13

by
András Némethi; Tamás László

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Let M be a rational homology sphere plumbed 3-manifold associated with a connected negative definite plumbing graph. We show that its Seiberg-Witten invariants equal certain coefficients of an equivariant multivariable Ehrhart polynomial. For this, we construct the corresponding polytopes from the plumbing graphs together with an action of the first homology of M, and we develop Ehrhart theory for them. At an intermediate level we define the `periodic constant' of multivariable series and...

Source: http://arxiv.org/abs/1211.2539v1

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56

Sep 22, 2013
09/13

by
Tamás László; András Némethi

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The lattice cohomology of a plumbed 3--manifold $M$ associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of $M$, and in the comparison of the topological properties with analytic ones when $M$ is realized as complex analytic singularity link. By definition, its computation is based on the (Riemann--Roch) weights of the lattice points of $\Z^s$, where $s$ is the number of vertices of the plumbing graph. The present article...

Source: http://arxiv.org/abs/1302.4716v2

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54

Sep 22, 2013
09/13

by
R. Garcia; A. Nemethi

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In the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special classes of polynomial maps which have, in some sense, nice properties at infinity. In this paper, we completely determine the complex algebraic monodromy at infinity for a special class of polynomial maps (which is complicated enough to show the nature of the general problem).

Source: http://arxiv.org/abs/alg-geom/9602009v1

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142

Jul 20, 2013
07/13

by
János Kollár; András Némethi

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Let X be a complex analytic space. A short analytic arc is a holomorphic map of the closed unit disc to X such that only the origin is mapped to a singular point. In contrast with the space of formal arcs studied by Nash, the moduli space of short analytic arcs usually has infinitely many connected components. We describe these for surface singularities, in terms of certain conjugacy classes of the fundamental group of the link. For quotient singularities (in any dimension), this gives a...

Source: http://arxiv.org/abs/1304.7853v2

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46

Sep 22, 2013
09/13

by
A. Dimca; A. Nemethi

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We consider an arbitrary polynomial map $f:{\mathbb C}^{n+1}\to {\mathbb C} $ and we study the Alexander invariants of ${\mathbb C}^{n+1}\setminus X$ for any fiber $X$ of $f$. The article has two major messages. First, the most important qualitative properties of the Alexander modules are completely independent of the behaviour of $f$ at infinity, or about the special fibers. Second, all the Alexander invariants of all the fibers of the polynomial $f$ are closely related to the monodromy...

Source: http://arxiv.org/abs/math/0201291v1

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67

Jun 28, 2018
06/18

by
Eugene Gorsky; András Némethi

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It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below: one in terms of the $h$-function, one in terms of the Alexander polynomial, and one in terms of the embedded resolution graph. They show that the set of L-space surgeries is...

Topics: Mathematics, Algebraic Geometry, Geometric Topology

Source: http://arxiv.org/abs/1509.01170

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50

Sep 19, 2013
09/13

by
Andras Nemethi; Agnes Szilard

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Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides the characteristic polynomial of the algebraic monodromy as well. Moreover, for any analytic germ g such that the pair (f,g) is an isolated complete intersection singularity, the (multiplicity system of the) open book decomposition of the boundary with binding...

Source: http://arxiv.org/abs/0909.0354v2

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53

Sep 19, 2013
09/13

by
Andras Nemethi; Tomohiro Okuma

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In the article we prove the Casson Invariant Conjecture of Neumann--Wahl for splice type surface singularities. Namely, for such an isolated complete intersection, whose link is an integral homology sphere, we show that the Casson invariant of the link is one-eighth the signature of the Milnor fiber.

Source: http://arxiv.org/abs/math/0610465v1

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4.0

Jun 30, 2018
06/18

by
András Némethi; Gergő Pintér

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A holomorphic germ \Phi: (C^2, 0) \to (C^3, 0), singular only at the origin, induces at the links level an immersion of S^3 into S^5. The regular homotopy type of such immersions are determined by their Smale invariant, defined up to a sign ambiguity. In this paper we fix a sign of the Smale invariant and we show that for immersions induced by holomorphic gems the sign-refined Smale invariant is the negative of the number of cross caps appearing in a generic perturbation of \Phi. Using the...

Topics: Mathematics, Algebraic Topology, Algebraic Geometry

Source: http://arxiv.org/abs/1404.2853

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53

Sep 22, 2013
09/13

by
Andras Nemethi; Claude Sabbah

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We prove that, for an analytic family of ``weakly tame'' regular functions on an affine manifold, the spectrum at infinity of each function of the family is semicontinuous in the sense of Varchenko.

Source: http://arxiv.org/abs/math/9805086v1

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Sep 19, 2013
09/13

by
András Némethi; Tomohiro Okuma

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We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the germs is a rational homology sphere. In the case of several sub-families we provide explicit formulas in terms of the Seifert invariants (generalizing results of Wagreich and VanDyke), and we also provide key examples showing that, in general, these invariants...

Source: http://arxiv.org/abs/0910.4035v2

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48

Sep 22, 2013
09/13

by
Maciej Borodzik; Andras Nemethi

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We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links, we reprove (in a slightly weaker version) a result obtained by Steenbrink and Varchenko on semicontinuity of spectrum at infinity. We also relate the spectrum at infinity of a polynomial with spectra of singular points of a chosen fiber.

Source: http://arxiv.org/abs/1101.5471v2

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45

Sep 21, 2013
09/13

by
Eugene Gorsky; András Némethi

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We construct a version of the lattice homology for plane curve singularities using the normalization of their components. We prove that the Poincare series of the associated graded homologies can be identified by an algebraic procedure with the motivic Poincare series. Hence, for a plane curve singularity the following objects carry the same information: the multi-variable Alexander polynomial, the multi-variable Hilbert series associated with the normalization, the motivic Poincare series, and...

Source: http://arxiv.org/abs/1301.7636v1

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120

Sep 17, 2013
09/13

by
Andras Nemethi; Liviu I. Nicolaescu

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We verify the conjecture formulated in math.AG/0111298 for suspension singularities of type $g(x,y,z)= f(x,y)+z^n$, where $f$ is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg-Witten invariant of the link $M$ of $g$, associated with the canonical $spin^c$ structure, equals $-\sigma(F)/8$, where $\sigma(F)$ is the signature of the Milnor fiber of $g$. In order to do this, we prove general splicing formulae for the Casson-Walker invariant and for the...

Source: http://arxiv.org/abs/math/0207018v1

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59

Sep 22, 2013
09/13

by
Andras Nemethi; Liviu I Nicolaescu

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We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we establish its validity for a large class of singularities: some rational and minimally elliptic (including the cyclic quotient and `polygonal') singularities, and Brieskorn-Hamm complete intersections. Some of the verifications are based on a result which describes...

Source: http://arxiv.org/abs/math/0111298v3

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54

Sep 22, 2013
09/13

by
Andras Nemethi; Liviu I. Nicolaescu

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This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data which can be read from a resolution graph of the singularity. Moreover, we also determine all the Reidemeister-Turaev sign-refined torsion of the link (associated with any spin^c structure) in terms of the Seifert invariants.

Source: http://arxiv.org/abs/math/0201120v1

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42

Sep 22, 2013
09/13

by
Andras Nemethi; Patrick Popescu-Pampu

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The oriented link of the cyclic quotient singularity $\mathcal{X}_{p,q}$ is orientation-preserving diffeomorphic to the lens space $L(p,q)$ and carries the standard contact structure $\xi_{st}$. Lisca classified the Stein fillings of $(L(p,q), \xi_{st})$ up to diffeomorphisms and conjectured that they correspond bijectively through an {\it explicit} map to the Milnor fibers associated with the irreducible components (all of them being smoothing components) of the reduced miniversal space of...

Source: http://arxiv.org/abs/0805.3449v2

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93

Sep 22, 2013
09/13

by
Andras Nemethi; Patrick Popescu-Pampu

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The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those...

Source: http://arxiv.org/abs/0906.2920v1

Performer: NÉMETHI FERENCZ; Berkes Béla Cigányzenekara (Népdal); Tenor; Kiséri. Digitized at 78 revolutions per minute. Four stylii were used to transfer this record. They are 3.8mil truncated conical, 2.3mil truncated conical, 2.8mil truncated conical, 3.3mil truncated conical. The preferred versions suggested by an audio engineer at George Blood, L.P. have been copied to have the more friendly filenames. Matrix number: W 109175 Catalog number: 10172-F Other IDs from the record include:...

Topics: 78rpm, Folk

Source: 78

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42

Sep 18, 2013
09/13

by
Maciej Borodzik; András Némethi; Andrew Ranicki

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We study the cobordism of manifolds with boundary, and its applications to codimension 2 embeddings $M^m\subset N^{m+2}$, using the method of the algebraic theory of surgery. The first main result is a splitting theorem for cobordisms of algebraic Poincar\'e pairs, which is then applied to describe the behaviour on the chain level of Seifert surfaces of embeddings $M^{2n-1} \subset S^{2n+1}$ under isotopy and cobordism. The second main result is that the $S$-equivalence class of a Seifert form...

Source: http://arxiv.org/abs/1211.5964v1

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3.0

Jun 30, 2018
06/18

by
Tamás László; János Nagy; András Némethi

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Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated with $\mathcal{T}$ and its counting functions, which encode rich topological information. Using the `periodic constant' of the series (with reduced variables) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant appears as the difference of...

Topics: Algebraic Geometry, Geometric Topology, Mathematics

Source: http://arxiv.org/abs/1702.06692

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Sep 22, 2013
09/13

by
Maciej Borodzik; András Némethi; Andrew Ranicki

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We use purely topological methods to prove the semicontinuity of the mod 2 spectrum of local isolated hypersurface singularities in $\mathbb{C}^{n+1}$, using Seifert forms of high-dimensional non-spherical links, the Levine--Tristram signatures and the generalized Murasugi--Kawauchi inequality obtained in earlier work for cobordisms of links.

Source: http://arxiv.org/abs/1210.0798v2

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Sep 20, 2013
09/13

by
Maciej Borodzik; András Némethi; Andrew Ranicki

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We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a topological assumption, a critical point in the interior of a Morse function can be moved to the boundary, where it splits into a pair of boundary critical points. As an application, we prove that every cobordism of manifolds with boundary splits as a union of left product cobordisms and right...

Source: http://arxiv.org/abs/1207.3066v3

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Jun 30, 2018
06/18

by
Tommaso de Fernex; János Kollár; András Némethi

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In 1978 Durfee conjectured various inequalities between the signature and the geometric genus of a normal surface singularity. Since then a few counter examples have been found and positive results established in some special cases. We prove a `strong' Durfee--type inequality for any smoothing of a Gorenstein singularity, provided that the intersection form the resolution is unimodular, and the conjectured `weak' inequality for all hypersurface singularities and for sufficiently large...

Topics: Complex Variables, Mathematics, Algebraic Geometry

Source: http://arxiv.org/abs/1411.1039

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3.0

Jun 28, 2018
06/18

by
Ádám Gyenge; András Némethi; Balázs Szendrői

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We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...

Topics: Representation Theory, Combinatorics, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1512.06848